For all doping, we find a dominant \(d\) -wave pairing symmetry for large \(t_c/K \)  or small \(K\) . But for low doping and moderate \(t_c/K\) , we obtain a \(\left( d+is\right) \) -wave pairing state that breaks the time-reversal
symmetry. This is different from the conventional picture based purely on the
\(t\) -\(J\)  model for cuprates, where the Heisenberg superexchange interaction
favors \(d\) -wave pairing [1]}. The \(s\) -wave pairing should be
ascribed to the Kondo coupling, which is an on-site spin exchange between
localized and conduction electrons [2]}. This is supported
by the extended \(s\) -wave solution at large doping for small \(t_c/K\)  or
strong Kondo coupling. It is the combination of both effects that gives rise
to the special \(\left( d+is\right) \) -wave superconductivity and represents a
genuine feature of the nickelate superconductivity differing from cuprates
or heavy fermions.
